# 信息来源： 暂无 　 发布日期: 2021-07-14　 浏览次数: _showDynClicks("wbnews", 1756464364, 1284)

Bollobàs and Scott conjectured that every graph $G$ has a balanced bipartite spanning subgraph $H$ such that for each $v\in V(G)$, $d_H(v)\geq (d_G(v)-1)/2$. In this talk, we show that every graphic sequence has a realization for which this Bollobàs-Scott conjecture holds, confirming a conjecture of Hartke and Seacrest. On the other hand, we use an infinite family of graphs to illustrate that $\lfloor (d_G(v)-1)/2 \rfloor$ (rather than $(d_G(v)-1)/2$) may have been the intended lower bound by Bollobàs and Scott. We also introduce other problems about vertex partitions of graphs.

颜娟，丽水学院副教授，“浙江省高校领军人才培养计划”高层次拔尖人才。于2009年在南京师范大学数学科学学院获博士学位，主要从事图的划分方面的研究，论文发表在《Journal of Combinatorial Theory, Series B》、 《Journal of Graph Theory》、《Discrete Mathematics》等国际权威学术期刊上。主持完成2项国家基金，曾应邀赴美国佐治亚理工大学访问。